5 papers
Gromov-Hausdorff distance and Jung constant of finite-dimensional normed spaces
Henry Adams, Semeon A. Bogatyi, Florian Frick +5
For a finite-dimensional normed space and a subset with finite Hausdorff distance from , we prove that the Gromov--Hausdorff distance between and is at least the…
Glioma C6: A Novel Dataset for Training and Benchmarking Cell Segmentation
Roman Malashin, Svetlana Pashkevich, Daniil Ilyukhin +4
We present Glioma C6, a new open dataset for instance segmentation of glioma C6 cells, designed as both a benchmark and a training resource for deep learning models. The dataset co…
Neural network task specialization via domain constraining
Roman Malashin, Daniil Ilyukhin
This paper introduces a concept of neural network specialization via task-specific domain constraining, aimed at enhancing network performance on data subspace in which the network…
The Fermat-Torricelli problem in normed spaces
Daniil A. Ilyukhin
The article studies a generalization of the classical Fermat-Torricelli problem to normed spaces of arbitrary finite dimension. Necessary and sufficient conditions for the uniquene…
The Fermat-Torricelli problem in the case of three-point sets in normed planes
D. A. Ilyukhin
In the paper the Fermat-Torricelli problem is considered. The problem asks a point minimizing the sum of distances to arbitrarily given points in d-dimensional real normed spaces.…